As I reported earlier, the change of address tool does not support HTTP to HTTPS migrations and John Mueller of Google said "just use normal 301s."
But how important is the change of address tool when migrating to a new domain name?
John Mueller responded to a Stack Exchange thread about a site migration and said:
I'd use the setting right away -- but make sure you have the 301 redirects in place ASAP too (especially for the most important pages). This setting helps us to confirm that you really want to transfer everything (all signals that we've collected over the years) over to the new domain. It just speeds things up a tiny bit, essentially.
So John said in terms of using the change of address tool:
(1) Use it "right away"
(2) The tool helps "confirm" that you want to transfer everything.
(3) It speeds things up a tiny bit
So those who migrate from HTTP to HTTPS do not benefit from the change of address tool.
Forum discussion at Stack Exchange.